A regular polygon is an n-sided polygon in which all sides are of the same length and all angles have the same degree (i.e., the polygon is both equilateral and equiangular). The formula for computing the area of a regular polygon is:

$$\text { Area }=\frac{n \times s^2}{4 \times \tan \left(\frac{\pi}{n}\right)}$$

Write a method that returns the area of a regular polygon using the following header:

public static double area(1nt $\mathrm{n}$, double side)

Write a main method that prompts the user to enter the number of sides and the side of a regular polygon and displays its area.

A regular polygon is an n-sided polygon in which all sides are of the same length and all angles have the same degree (i.e., the polygon is both equilateral and equiangular). The formula for computing the area of a regular polygon is

Here, s is the length of a side. Write a program that prompts the user to enter the number of sides and their length of a regular polygon and displays its area. Here is a sample run:

Enter the number of sides: 5 <enter>
Enter the side: 6.5 <enter>
The area of the polygon is 73.69017017488385

Then, Rewrite it using the following function to return the area of a regular polygon:

def area(n, side):

(Geometry: area of a regular polygon) A regular polygon is an $n$-sided polygon in which all sides are of the same length and all angles have the same degree (i.e., the polygon is both equilateral and equiangular). The formula for computing the area of a regular polygon is

$$\text { Area }=\frac{n \times s^2}{4 \times \tan \left(\frac{\pi}{n}\right)}$$

Here, $s$ is the length of a side. Write a program that prompts the user to enter the number of sides and their length of a regular polygon and displays its area. Here is a sample run:

Enter the number of sides: 5 
Enter the side: 6.5
The area of the polygon is 72.69017017488385

(Geometry: n-sided regular polygon) In an n-sided regular polygon, all sides have the same length and all angles have the same degree (i.e., the polygon is both equilateral and equiangular). Design a class named RegularPolygon that contains: A private int data field named n that defines the number of sides in the polygon with default value 3.

Write a class that contains the following two methods:

/** Convert from feet to meters */
public static double footToMeter(double foot)
/** Convert from meters to feet */
public static double meterToFoot(double meter)

The formula for the conversion is:

meter = 0.305 * foot
foot = 3.279 * meter

Write a test program that invokes these methods to display the following tables:

Feet      Meters     |     Meters        Feet
1.0       0.305      |      20.0        65.574
2.0       0.610      |      25.0        81.967
...
9.0       2.745      |      60.0       196.721
10.0      3.050      |      65.0       213.115

Write a class that contains the following two methods:

/** Convert from feet to meters */
public static double footToMeter(double foot)

/** Convert from meters to feet */
public static double meterToFoot(double meter)

The formula for the conversion is:

$$meter = 0.305 * foot$$

$$foot = 3.279 * meter$$

Write a test program that invokes these methods to display the following tables:

Feet        Meters     |   Meters       Feet
 1.0         0.305     |   20.0         65.574
 2.0         0.610     |   25.0         81.967
...
 9.0         2.745     |   60.0        196.721
10.0         3.050     |   65.0        213.115

Write a program that prompts the user to enter two strings and tests whether the second string is a substring of the first string. Suppose the neighboring characters in the string are distinct. (Don’t use the indexOf method in the String class.) Analyze the time complexity of your algorithm. Your algorithm needs to be at least $O(n)$ time. Here is a sample run of the program:

Enter a string s1: Welcome to Java <enter>
Enter a string s2: come <enter>
matched at index 3

Write a function that checks whether two words are anagrams. Two words are anagrams if they contain the same letters. For example, silent and listen are anagrams. The header of the function is:

def isAnagram(s1, s2):

(Hint: Obtain two lists for the two strings. Sort the lists and check if two lists are identical.)

Write a test program that prompts the user to enter two strings and, if they are anagrams, displays is an anagram; otherwise, it displays is not an anagram.

Write a program that asks the user to enter a number of seconds. - There are 60 seconds in a minute. If the number of seconds entered by the user is greater than or equal to 60, the program should display the number of minutes in that many seconds. - There are 3,600 seconds in an hour. If the number of seconds entered by the user is greater than or equal to 3,600, the program should display the number of hours in that many seconds. - There are 86,400 seconds in a day. If the number of seconds entered by the user is greater than or equal to 86,400, the program should display the number of days in that many seconds.

Write a program that asks the user to enter a number of seconds and works as follows:

• There are 60 seconds in a minute. If the number of seconds entered by the user is greater than or equal to 60, the program should display the number of minutes in that many seconds.

• There are 3,600 seconds in an hour. If the number of seconds entered by the user is greater than or equal to 3,600, the program should display the number of hours in that many seconds.

• There are 86,400 seconds in a day. If the number of seconds entered by the user is greater than or equal to 86,400, the program should display the number of days in that many seconds.

A pentagonal number is defined as n(3n–1)/2 for n = 1, 2, . . ., and so on. Therefore, the first few numbers are 1, 5, 12, 22, . . . . Write a method with the following header that returns a pentagonal number: public static int getPentagonalNumber(int n) Write a test program that uses this method to display the first 100 pentagonal numbers with 10 numbers on each line.

The area of a pentagon can be computed using the following formula:

$$\text { Area }=\frac{5 \times s^2}{4 \times \tan \left(\frac{\pi}{5}\right)}$$

Write a method that returns the area of a pentagon using the following header:

public static double area(double side)

Write a main method that prompts the user to enter the side of a pentagon and displays its area.

You should add the static keyword in the place of ? in line ______ in the following code:

public class Test {
  private int age;
  
  public ? int square(int n) {
    return n * n;
  }
  
  public ? int getAge() {
    return age;
  }
}

a. in line 4

b. in line8

c. in both line 4 and line 8

d. none

Variables that are shared by every instance of the class are ____________ variables.

A) private

B) instance

C) class

D) static